Question 3 Given that -6

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Question 3 Given that  -6 <= x <= 3 and  1 <= y <= 5, find the greatest possible value of  x^(2)+y^(2).

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Given Ranges: We are given the ranges for x and y: -6 <= x <= 3 1 <= y <= 5 We need to find the greatest possible value of the expression x^(2)+y^(2). To maximize the expression, we need to find the maximum values of x^(2) and y^(2) within the given ranges.Maximize x^(2): For x^(2) to be maximum, we need to find the value of x that gives the largest square within the range -6 <= x <= 3. Squaring a negative number or a positive number both give a positive result, and the square of a larger absolute value is greater. Therefore, the maximum value of x^(2) occurs at x = -6. Calculate x^(2) when x = -6. (-6)^(2) = 36Maximize y^(2): For y^(2) to be maximum, we need to find the value of y that gives the largest square within the range 1 <= y <= 5. Since squaring a number gives a positive result and the function y^(2) is increasing for positive y, the maximum value of y^(2) occurs at y = 5. Calculate y^(2) when y = 5. 5^(2) = 25Calculate Maximum Value: Now, we add the maximum values of x^(2) and y^(2) to find the greatest possible value of the expression x^(2)+y^(2). 36 (from x^(2)) + 25 (from y^(2)) = 61

Question $3$ $\newline$ Given that $-6 \leq x \leq 3$ and $1 \leq y \leq 5$ , find the greatest possible value of $x^{2}+y^{2}$ .

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Question 333\newlineGiven that −6≤x≤3 -6 \leq x \leq 3 −6≤x≤3 and 1≤y≤5 1 \leq y \leq 5 1≤y≤5, find the greatest possible value of x2+y2 x^{2}+y^{2} x2+y2.

Question $3$ $\newline$ Given that $-6 \leq x \leq 3$ and $1 \leq y \leq 5$ , find the greatest possible value of $x^{2}+y^{2}$ .